The Structure of Perfect Optimal Models with a Two-Category Class Variable and Four or Fewer Endpoints

Paul R. Yarnold

Optimal Data Analysis, LLC

An optimal model has a specific geometric configuration defined by the number of attributes (“independent variables”—schematically illustrated using circles) and endpoints (defined by response on attribute—indicated by rectangles). Branches direct attributes to endpoints via an if/then/else-based decision rule identified by the (ODA/CTA/novometric) algorithm and operationalized vis-à-vis numerical thresholds or categorical rosters which explicitly maximize (weighted) classification accuracy. In hopes of aiding in the visualization, pursuit and discovery of perfectly accurate statistical classification models, this paper presents schematic diagrams which correspond to combinations of number of attributes and endpoints that are possible for a range of optimal models commonly reported.

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Value-Added by ODA vs. Chi-Square

Paul R. Yarnold

Optimal Data Analysis, LLC

Beyond identifying the most accurate classification model which exists for the sample, and estimating cross-generalizability vis-à-vis jackknife, hold-out and/or other validity methods, ODA provides the exact one- or two-tailed P-value, the sensitivity and predictive value for each category of the class variable, and the effect strength corrected for chance.

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Maximum-Precision Markov Transition Table: Successive Daily Change in Closing Price of a Utility Stock

Paul R. Yarnold

Optimal Data Analysis, LLC

Research seeking to increase the accuracy of traditional Markov analysis-based models, which assess the outcome (class) variable as a two-category variable, studies the use of over-time weighting schemes. This paper demonstrates how to maximize precision of the class variable by using ODA to weight each individual “observation” (event) in the transition table by its corresponding exact absolute change-in-value.

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